S-duality in N=4 supersymmetric gauge theories

The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle $\theta$. This extended S-duality conjecture includes the case when the unbroken gauge group is non-abelian and a definite prediction for the spectrum of dyons results.